Simplify the following expression: $a = \dfrac{z + 4}{z - 9} \div 9$
Solution: Dividing by a number is the same as multiplying by its inverse. $a = \dfrac{z + 4}{z - 9} \times \dfrac{1}{9}$ When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{(z + 4) \times 1} {(z - 9) \times 9}$ $a = \dfrac{z + 4}{9z - 81}$